Volume 8, Issue 2
Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications

Meirav Galun, Ronen Basri & Irad Yavneh

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 283-312.

Published online: 2015-08

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  • Abstract

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.

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@Article{NMTMA-8-283, author = {}, title = {Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {2}, pages = {283--312}, abstract = {

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w14si}, url = {http://global-sci.org/intro/article_detail/nmtma/12411.html} }
TY - JOUR T1 - Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 283 EP - 312 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.w14si UR - https://global-sci.org/intro/article_detail/nmtma/12411.html KW - AB -

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.

Meirav Galun, Ronen Basri & Irad Yavneh. (2020). Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications. Numerical Mathematics: Theory, Methods and Applications. 8 (2). 283-312. doi:10.4208/nmtma.2015.w14si
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